One Line, Nexus and Infinity Loop: MyRin Path Puzzles Explained

MyRin has three puzzles about paths. In One Line you trace a figure in a single stroke. In Nexus you connect pairs of coloured dots without crossing. In Infinity Loop you rotate pieces of wire until power flows through the whole circuit.

You can solve all three by trying things until something works. But each puzzle has one central idea that, once you see it, replaces most of the guessing. This article is about those three ideas.

One Line: count the edges first

One Line, called Ippitsugaki in the app, from the Japanese for "written in one stroke", asks you to trace every edge of a figure without lifting your finger and without using any edge twice.

The key idea is almost three hundred years old. In 1736, the mathematician Leonhard Euler studied a puzzle about the bridges of Königsberg: could you walk through the city crossing each of its seven bridges exactly once? He showed that the answer depends only on how many lines meet at each point.

Call the number of edges at a point its degree. Then:

• If every point has an even degree, you can trace the figure starting anywhere, and you will finish where you started.
• If exactly two points have an odd degree, you must start at one of them and finish at the other.
• If more than two points have an odd degree, it cannot be done.

So before you draw anything, count. Points where three or five edges meet are the only possible start and end points. That one check removes most of the failed attempts.

The second idea: save bridges for last. A bridge is an edge that is the only connection between two parts of the figure. If you cross it too early, you cannot get back to the part you left behind. When you get stuck halfway, this is almost always why.

See our One Line guide for worked examples.

Nexus: every cell must be filled

Nexus asks you to connect each pair of matching dots with a path. Paths cannot cross, and every cell in the grid must be covered.

That last rule is the key idea, and it is the one beginners forget. Without it, the puzzle would be easy: draw short, direct paths and stop. With it, many paths that look sensible are impossible because they would leave a cell or a pocket of cells that no colour can reach.

Practical techniques that follow from it:

• Start at the edges and corners. A dot in a corner has only two directions to go. Its path is usually forced for the first few steps.
• Hug the walls. Paths that run along the edge of the grid rarely trap cells. Paths that cut through the middle often do.
• Look for pockets. If a small area of the grid can only be reached by one colour, that colour must fill it.
• Watch out for isolated cells. A single empty cell surrounded by other paths means something has gone wrong. Back up to the last choice you made.

Our Nexus guide goes deeper.

Infinity Loop: let the edges decide

Infinity Loop gives you a grid of wire pieces, straight lines, corners, T-junctions and dead ends. You tap a piece to turn it a quarter turn. Pieces only light up when power actually reaches them from a source through wires that meet on both sides, so the spreading glow is your only feedback. The goal is to light every lamp.

The key idea is that pieces on the border have fewer legal positions. A wire cannot point off the edge of the grid. A corner piece in a corner of the board can usually fit only one way. Each piece you settle then limits the piece next to it, and the solution spreads inward.

Useful details:

• Dead ends are the most informative pieces. A piece with a single arm has to point towards one specific neighbour. Place those before anything ambiguous.
• Straight pieces have two positions, not four. Turning a straight twice brings it back to where it was. Noticing this halves the work.
• Follow the light. Glowing wire is already solved. Extend it one piece at a time rather than turning pieces at random elsewhere on the board.

See the Infinity Loop guide for more.

What the three have in common

The three puzzles look different, but they share a way of thinking: start where the choices are fewest. In One Line that means the odd-degree points. In Nexus it means corners and walls. In Infinity Loop it means the border and the dead ends.

This is one of the most useful habits in any logic puzzle. Instead of starting wherever your eye lands, look for the most constrained part of the problem. Solving it gives you information about everything around it. It works in sudoku, in Hashi, in Nurikabe, and in most problems outside games too.

Which one to play

• A quick, satisfying solve: One Line. Once you know the counting rule, most figures fall in under a minute.
• Spatial planning: Nexus. You are always thinking about how one path affects the space left for the others.
• A calm, step-by-step puzzle: Infinity Loop. The light gives you steady feedback, and there is little guessing once you work from the edges.

All three are good choices when you want to think rather than race. For more on how MyRin's puzzles are designed to get harder, see our article on how we design puzzle difficulty.